基于分数阶环境热浴的非各态历经判据研究

卢宏; 吕艳; 包景东

doi:10.7498/aps.64.170502

摘要

本文从分数阶谱形式的气固耦合模型出发, 理论推导出具有幂律记忆核的广义朗之万方程. 研究气体分子在自由场和简谐势场中的动力学演化和长时渐进行为, 着重分析三种各态历经判据: Khinchin判据、Lee判据以及内在判据和外在表现的适用性. 研究结果表明: Khinchin判据适用于广义朗之万方程描述的所有扩散和输运过程; Lee判据并不适用于布朗运动, 只能用来区分不同类型的扩散过程; 而内在判据和外在表现不仅能够把非各态历经分为两类, 同时可以揭示非各态历经的物理内在根源.

关键词:

Abstract

The generalized Langevin equation with a power law memory kernel is derived via the gas/solid-surface model with fractional heat bath. Using Lapalce transformation, the dynamic evolution and long-time asymptotic behaviors of the gas particles occurring either in free or harmonic potentials are then investigated. In particular, the validity of three kinds of ergodic criteria is analyzed in detail, including the Khinchin criterion, Lee criterion, and the intrinsic and external behaviors. It is found that the Khinchin criterion holds for all ranges of diffusion and transport processes described by a generalized Langevin equation. Lee criterion is just applied to distinguish diffusion processes. Meanwhile, the intrinsic criterion and external behaviors can not only divide the nonergodicity into two classes but also reveal the underlying physical origins.

Keywords:

作者及机构信息

1.
西华大学理学院物理系, 成都 610039;

2.
太原科技大学应用科学学院, 太原 030024;

3.
北京师范大学物理系, 北京 100875

通信作者: 卢宏, bj_luhong@163.com

基金项目: 四川省教育厅青年基金(批准号: 13233683)、西华大学校级重点科研项目(批准号: Z1123330)和西华大学先进计算中心实验室基金资助的课题.

Authors and contacts

1.
School of Science, Xihua University, Chengdu 610039, China;

2.
School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China;

3.
Department of Physics, Beijing Normal University, Beijing 100875, China

Corresponding author: Lu Hong, bj_luhong@163.com

Funds: Project supported by the Natural Science Foundation of the Education Department of Sichuan Province, China (Grant No. 13233683), the Key Scientific Research Foundation of Xihua University (Grant No. Z1123330), and the Foundation of Key Laboratory of Advanced Scientific Computation, Xihua University, China.

参考文献

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施引文献

[1]	Tamm M V, Nazarov L I, Gavrilov A A, Chertovich A V 2015 Phys. Rev. Lett. 114 178102
[2]	Guo G, Bittig A, Uhrmacher A 2015 J. Comput. Phys. 288 167
[3]	Hu W Y, Shao Y Z 2014 Acta Phys. Sin. 63 238202 (in Chinese) [胡文勇, 邵元智 2014 63 238202]
[4]	Lin F, Bao J D 2008 Acta Phys. Sin. 57 696 (in Chinese) [林方, 包景东 2008 57 696]
[5]	Montroll E, Weiss G 1965 J. Math. Phys. Lett. 6 167
[6]	Viñales A D, Despósito M A 2006 Phys. Rev. E 73 016111
[7]	Burov S, Barkai E 2008 Phys. Rev. Lett. 100 070601
[8]	Amblard F, Maggs A C, Yurke B, Pargellis A N, Leibler S 1996 Phys. Rev. Lett. 77 4470
[9]	Gu Q, Schiff E A, Grebner S, Wang F, Schwara R 1996 Phys. Rev. Lett. 76 3196
[10]	Sciortion F, Tartaglia P 1997 Physcia A 236 140
[11]	Stephenson J 1995 Physica A 222 234
[12]	Lu H, Qin L, Bao J D 2009 Acta Phys. Sin. 58 8127 (in Chinese) [卢宏, 覃莉, 包景东 2009 58 8127]
[13]	Lu H, Bao J D 2013 Chin. Phys. Lett. 30 010502
[14]	Brokmann X, Hermier J P, Messin G, Deebiolles P, Bouchard J P, Dahan M 2003 Phys. Rev. Lett. 90 120601
[15]	Saubamea B, Leduc M, Cohen-Tannoudji C 1999 Phys. Rev. Lett. 83 3796
[16]	Lutz E 2004 Phys. Rev. Lett. 93 190602
[17]	Papoulis A 1965 Probability, Random Variables and Stochastic Processes (New York: McGraw-Hill)
[18]	Lapas L C, Morgado R, Vainstein M H, Rubí J M, Oliveirs F A 2008 Phys. Rev. Lett. 101 230602
[19]	Lee M H 2007 Phys. Rev. Lett. 98 110403
[20]	Bai Z W, Bao J D, Song Y L 2005 Phys. Rev. E 72 061105
[21]	Bao J D, Hänggi P, Zhuo Y Z 2005 Phys. Rev. E 72 061107
[22]	Bao J D, Zhuo Y Z, Oliveira F A, Hänggi P 2006 Phys. Rev. E 74 061111
[23]	Kupferman R 2004 J. Stat. Phys. 114 291
[24]	Mainardia F, Goren R 2000 J. Comput. Appl. Math. 118 283

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